Is feature engineer an important step for a deep learning approach?
From what I believe, feature engineering is important, it's a part of the job of ML network designer.
Network designing involves

Feature engineering: What should be in the input to the network, as processed from similar or totally different data
Deciding network shape, layer shapes, types of neurons in layers, etc.
Feature engineering again (but labels), in the output, what should the output be, either regression values or classes

And possibly also tasks rather simple as mentioned in the question: filling missing values, normalising data, create pre-feeding normalisation steps in code, etc.